The scaling in the previous equation is clearly unfavorable compared even with the trapezoidal rule. We saw that the trapezoidal rule carries a truncation error $$\mathrm{error}\sim O(h^2),$$ with $h$ the step length. In general, methods based on a Taylor expansion such as the trapezoidal rule or Simpson's rule have a truncation error which goes like $\sim O(h^k)$, with $k \ge 1$. Recalling that the step size is defined as $h=(b-a)/N$, we have an error which goes like $$\mathrm{error}\sim N^{-k}.$$